Automatic grid-connection control method for high-altitude platform air-pumping unit based on LADRC
By using the LADRC-based control method, automatic grid connection of the high-altitude air extraction unit was achieved, which solved the problem of low automation in the existing air extraction system, improved grid connection efficiency and safety, reduced pressure ratio fluctuations, and adapted to various operating conditions.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Patents(China)
- Current Assignee / Owner
- AECC SICHUAN GAS TURBINE RES INST
- Filing Date
- 2022-08-31
- Publication Date
- 2026-04-21
AI Technical Summary
The existing high-altitude test exhaust system has a low degree of automation and low efficiency of manual operation, which affects the test efficiency and cannot meet the continuous simulation requirements of the air working environment of aero engines. Furthermore, the pressure ratio fluctuation during the grid connection of the exhaust unit affects the test accuracy and safety.
The LADRC-based control method is adopted, and the anti-surge valve and main pipe regulating valve of the air extraction unit are controlled by the first and second LADRC controllers respectively to realize the automatic grid connection of the air extraction unit. This includes real-time acquisition of pressure values, calculation of pressure ratio, and adjustment of valve opening through the controller to achieve a fast and stable grid connection process.
It enables rapid and stable grid connection of the extraction unit, reduces pressure ratio fluctuations, improves grid connection efficiency and safety, reduces energy consumption and manpower requirements, and adapts to various grid connection conditions.
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Figure CN115614304B_ABST
Abstract
Description
Technical Field
[0001] This invention belongs to the field of high-altitude simulation technology for aero-engines, and particularly relates to an automatic grid-connected control method for high-altitude exhaust turbine units based on LADRC. Background Technology
[0002] A high-altitude test facility is a large-scale experimental facility capable of simulating high-altitude flight conditions of aero-engines on the ground. It is a crucial means of performance evaluation and verification during aero-engine development, primarily composed of systems such as an air supply system, a test chamber, an intake and exhaust system, and an extraction system. The extraction system is vital for ensuring the accuracy of the flight altitude simulation by pressurizing the negative-pressure exhaust gases entering the test chamber and releasing them into the atmosphere. The effectiveness of its grid-connected control directly impacts the safety and efficiency of the high-altitude test facility. Because the extraction system comprises multiple extraction units operating in parallel, it involves numerous devices and a complex structure, including multiple large-volume cavities and piping. Considering the nonlinear characteristics of the regulating valves and extraction units, the extraction system is a typical time-varying, high-inertia, and nonlinear control system with numerous adjustment components, making control challenging. In particular, the strong coupling between different units operating in parallel within the extraction system further increases the difficulty of automatic grid-connected control of the extraction units.
[0003] In recent years, to meet the testing requirements of continuous simulation of engine flight environments, high-altitude test gas supply systems have been rapidly expanding. While the gas supply capacity of these systems has been greatly improved, the grid connection of the extraction units still primarily relies on manual operation, resulting in low automation. Furthermore, with the increasing scale of high-altitude simulation test equipment, the problems of high human resource consumption and low efficiency of manual operation have become more prominent. Moreover, the manual operation (with valves and extraction units controlled by personnel) during gas extraction state switching or extraction unit exit from test mode not only affects overall test efficiency but also fails to adequately meet the requirements of continuous simulation of aero-engine in-flight operating environments. Therefore, research on automatic grid connection methods for extraction units is urgently needed. This paper designs an automatic grid connection control method for high-altitude test extraction units based on LADRC to achieve automatic grid connection of the extraction units, reduce pressure ratio fluctuations during the grid connection process, and enhance the adaptability of the extraction control system to nonlinear controlled objects. Summary of the Invention
[0004] In view of this, an automatic grid connection control method for high-altitude test pumping units based on LADRC is proposed to replace the current manual grid connection operation method of the pumping system. This method solves the technical problems of low efficiency in the existing grid connection process, which causes the pressure ratio fluctuation of the pumping unit to affect the test accuracy and the pressure ratio safety of the unit during the grid connection process.
[0005] An automatic grid-connected control method for high-altitude exhaust fan units based on LADRC is provided, applicable to experimental setups for high-altitude flight of aero-engines. The experimental setup includes an exhaust manifold, multiple exhaust fan units, a main exhaust manifold regulating valve, and each exhaust fan unit equipped with an anti-surge valve, an inlet valve, an exhaust valve, and a cooler. Pressure sensors are installed at the inlet and outlet of each exhaust fan unit. Each exhaust fan unit's anti-surge valve is equipped with a first LADRC controller, and the main exhaust manifold regulating valve is equipped with a second LADRC controller. An exhaust valve is installed on the outlet pipe of each exhaust fan unit, and an inlet valve is installed on the inlet pipe. The outlet of the inlet valve is also connected to the unit outlet and exhaust valve inlet via the anti-surge valve, and a cooler is installed thereon. The method includes:
[0006] Determine the total number of extraction units and the inlet and outlet pressure values for each extraction unit;
[0007] The inlet and outlet pressure values of each extraction unit are acquired in real time, the initial pressure ratio of the extraction unit is calculated, and the data is fed back to the first LADRC controller; the average inlet pressure of all units is acquired and fed back to the second LADRC controller in real time.
[0008] Determine the surge pressure ratio P for each pumping unit. c 1. Set the pressure ratio setpoint P of the air extraction unit during the transition from reflux state to throttling state. set and anti-surge valve pressure ratio P set And satisfy P set <P set <P c ;
[0009] When the extraction unit switches from reflux to throttling operation, the inlet valves of each unit automatically open, and the first LADRC controller acquires the current pressure ratio in real time and determines whether the current pressure ratio is greater than the set value P. set ,
[0010] If so, the anti-surge valve is adjusted upwards; otherwise, the anti-surge valve is adjusted downwards until the anti-surge valve is fully closed and the current pressure ratio P' meets P. set <P’<P set ;
[0011] Obtain the current operating status of all inlet valves and anti-surge valves of the extraction units, and enter the throttling to grid-connected operating state until all anti-surge valves are closed. Switch the main pipe regulating valve to automatic mode and obtain the extraction main pipe pressure set pressure ratio P. set Local atmospheric pressure p env Real-time calculation of the critical value of the extraction main pipe = p env / P setFurthermore, it is determined whether the average inlet pressure of all units is greater than the critical value of the extraction main pipe. If so, the main pipe regulating valve is adjusted to a smaller value; if not, the main pipe regulating valve is adjusted to a larger value until the average inlet pressure of all units is the same as the critical value of the extraction main pipe and all grid-connected unit inlet valves are fully open.
[0012] The beneficial effects of the present invention are as follows:
[0013] The automatic grid connection control method for high-altitude air extraction units based on LADRC enables rapid switching between reflux and throttling states, simultaneous or sequential grid connection of multiple extraction units, and minimizes pressure ratio fluctuations and speed during grid connection. It significantly improves the safety and efficiency of simultaneous grid connection of multiple extraction units, effectively saving energy consumption and personnel requirements, and reducing the impact of manual operation and external disturbances on the grid connection process. This automatic grid connection control method has strong versatility and can adapt to various grid connection conditions of high-altitude air extraction systems. Attached Figure Description
[0014] To more clearly illustrate the technical solutions of the embodiments of this disclosure, the drawings used in the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of this disclosure. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.
[0015] Figure 1 This is a simplified diagram of the overall structure of the air extraction system;
[0016] Figure 2 A simplified structural diagram of a single air extraction unit;
[0017] Figure 3 The valve operates during the process of switching the air extraction unit from reflux state to throttling state;
[0018] Figure 4 The control block diagram for the LADRC controller 1 of the anti-surge valve;
[0019] Figure 5 The valve operates during the process of switching the extraction unit from throttling mode to full-power extraction mode.
[0020] Figure 6 The control block diagram for LADRC controller 2 of the main exhaust manifold regulating valve;
[0021] Figure 7 The pressure ratio changes for three units simultaneously connected to the grid.
[0022] Figure 8 The voltage ratio changes of the three units connected to the grid successively;
[0023] Figure 9This is a physical diagram of the piping system for a single air extraction unit. Detailed Implementation
[0024] The embodiments of this disclosure will now be described in detail with reference to the accompanying drawings.
[0025] The following specific examples illustrate the implementation of this disclosure. Those skilled in the art can easily understand other advantages and effects of this disclosure from the content disclosed in this specification. Obviously, the described embodiments are only a part of the embodiments of this disclosure, and not all of them. This disclosure can also be implemented or applied through other different specific embodiments, and the details in this specification can also be modified or changed based on different viewpoints and applications without departing from the spirit of this disclosure. It should be noted that, in the absence of conflict, the following embodiments and features in the embodiments can be combined with each other. Based on the embodiments in this disclosure, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of this disclosure.
[0026] It should be noted that various aspects of embodiments within the scope of the appended claims are described below. It will be apparent that the aspects described herein can be embodied in a wide variety of forms, and any particular structure and / or function described herein is merely illustrative. Based on this disclosure, those skilled in the art will understand that one aspect described herein can be implemented independently of any other aspect, and two or more of these aspects can be combined in various ways. For example, any number of aspects set forth herein can be used to implement the device and / or practice the method. Additionally, this device and / or method can be implemented using other structures and / or functionalities besides one or more of the aspects set forth herein.
[0027] The specific implementation method of this embodiment is to first divide the grid connection process of the air extraction unit into two stages: reflux to throttling and throttling to grid connection (see the simplified diagram of the overall structure of the air extraction system). Figure 2 The LADRC controller 1 (first LADRC controller) is used to switch the pumping unit from a reflux state to a throttling state (valve action as follows). Figure 3 As shown, the control block diagram is as follows: Figure 4 As shown), LADRC controller 2 (the second LADRC controller) is used to switch the pumping unit from throttling mode to full-power pumping mode (valve action as shown). Figure 5 As shown, the control block diagram is as follows: Figure 6 As shown), the structure of the extraction unit is as follows: Figure 9 As shown.
[0028] The method described in this case is applicable to experimental setups for high-altitude flight of aircraft engines. The experimental setup includes a main exhaust manifold, multiple exhaust units, a main exhaust manifold regulating valve, an anti-surge valve on each exhaust unit, pressure sensors at the inlet and outlet of each exhaust unit, a first LADRC controller on each anti-surge valve, and multiple anti-surge valves connected in parallel. The main exhaust manifold regulating valve is equipped with a second LADRC controller. An exhaust valve is installed on the outlet pipe of each exhaust unit, and an inlet valve is installed on the inlet pipe. The outlet of the inlet valve is also connected to the unit outlet and the inlet of the exhaust valve via the anti-surge valve. A cooler is also installed thereon. The cooler's function is to reduce the temperature of the airflow from the unit outlet to the anti-surge valve to ambient temperature. The cooler includes:
[0029] S101: Determine the total number of extraction units required for grid connection, and the inlet and outlet pressure values of each extraction unit. The inlet and outlet pressure values of the extraction units are used to determine the unit pressure ratio. Each extraction unit is in a reflux state, with the inlet valve fully closed, the anti-surge valve fully open, and the vent valve fully open.
[0030] S102: Real-time acquisition of inlet and outlet pressure values of each extraction unit, calculation of the initial pressure ratio of the extraction unit, and feedback to the first LADRC controller; acquisition of the average inlet pressure of all units, and real-time feedback to the second LADRC controller;
[0031] S103: Determine the surge pressure ratio P for each pumping unit. c 1. Set the pressure ratio setpoint P of the air extraction unit during the transition from reflux state to throttling state. set and anti-surge valve pressure ratio P set And satisfy P set <P set <P c ;
[0032] S104: When the extraction unit switches from reflux to throttling, the current pressure ratio is obtained, and it is determined whether the current pressure ratio is greater than the set value P. set ,
[0033] If so, the anti-surge valve should not be adjusted larger; otherwise, the anti-surge valve should be adjusted smaller until the anti-surge valve is fully closed and the current pressure ratio P' meets the requirement of P. set <P’<P set ;
[0034] S105: Obtain the current operating status of all inlet valves and anti-surge valves of all extraction units, and enter the throttling to grid-connected operating state until all anti-surge valves are closed. The main pipe regulating valve switches to automatic mode, and obtains the extraction main pipe pressure set pressure ratio P. set Local atmospheric pressure p env Calculate the critical value of the extraction main pipe = penv / P set The current average inlet pressure of all extraction units is determined, and it is determined whether the average inlet pressure of all units is greater than the critical value of the extraction main pipe. If so, the main pipe regulating valve is adjusted to a smaller value; if not, the main pipe regulating valve is adjusted to a larger value, until the pressure value of the extraction main pipe is the same as the critical value of the extraction main pipe and all unit inlet valves are fully open.
[0035] Furthermore, methods for controlling the synchronization of the extraction unit are also included:
[0036] Obtain the average pressure ratio of all current extraction units, and determine whether the pressure ratio of the current extraction unit is greater than the average pressure ratio. If so, it is determined that the inlet valve of the current extraction unit is delayed, and the inlet valves of other extraction units remain open until the pressure ratio of the current extraction unit equals the average pressure ratio, and then they act synchronously. If not, it is determined that the inlet valve of the current extraction unit is activated prematurely, and the inlet valve of the current extraction unit continues to be open, while the other extraction units remain in their current state without action until the pressure ratio of the current extraction unit is the same as the average pressure ratio, and then they act synchronously.
[0037] As a specific implementation method provided in this case, it also includes delay calculation and anti-interference calculation of the first LADRC controller. Specifically, the first LADRC controller includes a first extended state observer and a first linear state error feedback controller. The first extended state observer performs real-time observation of the unit pressure ratio, dynamic changes, and system disturbances during the return-to-throttling process, effectively extracting its dynamic information and transmitting it to the first linear state error feedback controller. The first linear state error feedback controller generates control quantities based on the dynamic changes in the unit pressure ratio and system disturbance information to adjust the anti-surge valve opening for rapid compensation and suppression of disturbances, achieving high-precision control of the unit pressure ratio, wherein:
[0038] The linear state error feedback control rate of the first linear state error feedback controller is:
[0039]
[0040] Where e1 is the deviation between the actual pressure ratio obtained through the first expansion state observer and the compressor pressure ratio setpoint, and u1 is the control output of LADRC controller 1. This is an estimate of the pumping unit pressure ratio P obtained using the first extended state observer. for The estimated value of the derivative, b1 is the disturbance estimate, and b1 is the controller gain. This is the control bandwidth of the first LADRC controller. The first extended state observers (e1 and e2) observe the disturbance x1 and suppress the disturbance, including internal and external disturbances, to ensure the stability of the unit.
[0041] The method for operating the first extended state observer satisfies:
[0042] Where e2 is the deviation between the estimated pressure ratio of the extraction unit obtained using the first extended state observer and the measured pressure ratio of the extraction unit. This refers to the LESO1 observation bandwidth.
[0043] As a specific implementation method provided in this case, the second LADRC controller includes a second expanded state observer and a second linear state error feedback controller. The second expanded state observer monitors in real time the magnitude, dynamic changes, and system disturbances of the average inlet pressure of all units participating in grid connection during the throttling-to-grid connection process, effectively extracting dynamic information and transmitting it to the second linear state error feedback controller. The second linear state error feedback controller generates control quantities based on the dynamic changes of the average inlet pressure of all units and system disturbance information to adjust the opening of the main pipe regulating valve for rapid compensation and suppression of disturbances, achieving high-precision control of the average inlet pressure of all units and ensuring stable pressure ratios and safe operation of each unit. Wherein:
[0044] The linear state error feedback control law of the second linear state error feedback controller satisfies:
[0045] Where e3 is the average compressor inlet pressure of all grid-connected extraction units obtained using the second extended state observer. The deviation between the estimated value and the set value of the second LADRC controller, u2 is the control output. The average inlet pressure of the compressor of each extraction unit obtained using the second expansion state observer. The estimated value, express The estimated value of the differential. b1 is the disturbance estimate, and b2 is the controller gain. This is the control bandwidth of the second LADRC controller;
[0046] The method for operating the second extended state observer satisfies:
[0047] Where e4 represents the average pressure before the compressor of all pumping units participating in grid connection. The deviation between the measured value and the estimated value, This represents the observation bandwidth of the second extended state observer.
[0048] To ensure stable pressure in the main extraction pipe, the inconsistent movement time characteristics of each inlet valve during the grid connection of multiple units cause disturbances to the main pipe pressure. This control method suppresses these disturbances and ensures the accuracy of the overall experiment.
[0049] Implementation effect
[0050] Based on a Matlab / Simulink model of a high-altitude air extraction unit, simulation verification of automatic grid-connected control using LADRC was conducted. The simulation verification was divided into two scenarios: simultaneous grid connection of three units and grid connection of two units followed by connection of one unit. Figure 7 , Figure 8 The grid connection results show that the pressure ratio control of the three units is stable during the grid connection process in both cases, and is within the safe pressure ratio range of 3 to 8. This indicates that the control method is effective and can realize the automatic grid connection of multiple extraction units with good control effect.
[0051] Scenario 1 (Three units connected to the grid simultaneously): The three extraction units have identical performance, and the anti-surge valves and inlet valves are connected to the grid simultaneously in perfect synchronization. The simulation results are as follows: Figure 7 As shown, the pressure ratios of each unit are stable. The pressure ratio of extraction unit 1 is 4.68–5.63, the pressure ratio of extraction unit 2 is 4.30–5.53, and the pressure ratio of extraction unit 3 is 4.33–5.56.
[0052] Scenario 2 (Two units connected to the grid first, then one unit): The flow rates of the three units differ; the flow coefficient of unit 2 is 5% higher than that of unit 1, and the flow coefficient of unit 3 is 5% lower than that of unit 1; the speed of the anti-surge valve actuator in unit 2 is 5% faster than that in unit 1, and the speed of the anti-surge valve actuator in the extraction unit 3 is 5% slower than that in unit 1. Simulation results are as follows... Figure 8 As shown, during grid connection, the pressure ratio of extraction unit 1 is 4.35–5.69, the pressure ratio of unit 2 is 4.55–5.56, and the maximum pressure ratio of extraction unit 3 is 4.90–5.68.
[0053] In summary, the automatic grid connection control method for high-altitude air extraction units based on LADRC can achieve simultaneous or sequential grid connection of multiple air extraction units, with minimal pressure ratio fluctuations and rapid connection speed, thus improving grid connection efficiency and safety. This automatic grid connection control method has strong versatility and can adapt to various grid connection conditions of high-altitude air extraction systems.
[0054] The above are merely specific embodiments of this disclosure, but the scope of protection of this disclosure is not limited thereto. Any variations or substitutions that can be easily conceived by those skilled in the art within the scope of the technology disclosed in this disclosure should be included within the scope of protection of this disclosure. Therefore, the scope of protection of this disclosure should be determined by the scope of the claims.
Claims
1. An automatic grid-connected control method for high-altitude air extraction units based on LADRC, applicable to experimental devices for high-altitude flight of aero-engines, the experimental device comprising an extraction main pipe, multiple air extraction units, a main pipe regulating valve, each air extraction unit being equipped with an anti-surge valve, an inlet valve, an exhaust valve, and a cooler, characterized in that, Pressure sensors are installed at the inlet and outlet of each extraction unit. Each extraction unit's anti-surge valve is equipped with a first LADRC controller, and the main regulating valve is equipped with a second LADRC controller. An vent valve is installed on the outlet pipeline of the extraction unit, and an inlet valve is installed on the inlet pipeline. The outlet of the inlet valve is also connected to the unit outlet and the exhaust valve inlet via the anti-surge valve, and a cooler is installed thereon. The method includes: Determine the total number of extraction units required for grid connection, and the inlet and outlet pressure values of each extraction unit; The system acquires the inlet and outlet pressure values of each extraction unit in real time, calculates the initial pressure ratio of each extraction unit, and feeds it back to the first LADRC controller; it also acquires the average inlet pressure of all units and feeds it back to the second LADRC controller in real time. Determine the surge pressure ratio P for each pumping unit. c 1. Set the pressure ratio setpoint P of the air extraction unit during the transition from reflux state to throttling state. set and anti-surge valve pressure ratio P set And satisfy P set <P set <P c ; When the extraction unit switches from reflux to throttling operation, the inlet valves of each unit automatically open, and the first LADRC controller acquires the current pressure ratio in real time and determines whether the current pressure ratio is greater than the set value P. set , If so, the anti-surge valve is adjusted upwards; otherwise, the anti-surge valve is adjusted downwards until the anti-surge valve is fully closed and the current pressure ratio P' meets P. set <P’<P set ; Obtain the current operating status of all inlet valves and anti-surge valves of the extraction units, and enter the throttling to grid-connected operating state until all anti-surge valves are closed. Switch the main pipe regulating valve to automatic mode and obtain the extraction main pipe pressure set pressure ratio P. set Local atmospheric pressure p env Real-time calculation of the critical value of the extraction main pipe = p env / P set Furthermore, it is determined whether the average inlet pressure of all units is greater than the critical value of the extraction main pipe. If so, the main pipe regulating valve is adjusted to a smaller value; if not, the main pipe regulating valve is adjusted to a larger value until the average inlet pressure of all units is the same as the critical value of the extraction main pipe and all grid-connected unit inlet valves are fully open.
2. The automatic grid connection control method for high-altitude air extraction units based on LADRC according to claim 1, characterized in that, It also includes methods for controlling the synchronization of the air extraction unit: Obtain the average pressure ratio of all current extraction units, and determine whether the pressure ratio of the current extraction unit is greater than the average pressure ratio. If so, it is determined that the inlet valve of the current extraction unit is delayed, and the inlet valves of other extraction units remain open until the pressure ratio of the current extraction unit equals the average pressure ratio, and then they act synchronously. If not, it is determined that the inlet valve of the current extraction unit is activated prematurely, and the inlet valve of the current extraction unit continues to be open, while the other extraction units remain in their current state without action until the pressure ratio of the current extraction unit is the same as the average pressure ratio, and then they act synchronously.
3. The automatic grid-connected control method for high-altitude air extraction units based on LADRC according to claim 2, characterized in that, The anti-surge valves are arranged in parallel.
4. The automatic grid-connected control method for high-altitude air extraction units based on LADRC according to claim 2, characterized in that, The first LADRC controller includes a first extended state observer and a first linear state error feedback controller, wherein: the first extended state observer monitors the unit pressure ratio, dynamic changes, and system disturbances in real time during the return-to-throttling process, effectively extracts its dynamic information, and transmits it to the first linear state error feedback controller; the first linear state error feedback controller generates control quantities based on the dynamic changes in the unit pressure ratio and system disturbance information to adjust the anti-surge valve opening for rapid compensation and disturbance suppression, thereby achieving high-precision control of the unit pressure ratio, wherein: The linear state error feedback control rate of the first linear state error feedback controller is: Where e1 is the deviation between the actual pressure ratio obtained through the first expansion state observer and the compressor pressure ratio setpoint, and u1 is the control output of the first LADRC controller. This is an estimate of the pumping unit pressure ratio P obtained using the first extended state observer. for The estimated value of the derivative, Here, b1 is the disturbance estimate, and b1 is the gain of the first LADRC controller. The control bandwidth of the first LADRC controller; The method for operating the first extended state observer satisfies: Where e2 is the deviation between the estimated pressure ratio of the extraction unit obtained using the first extended state observer and the measured pressure ratio of the extraction unit. This refers to the LESO1 observation bandwidth.
5. The automatic grid-connected control method for high-altitude air extraction units based on LADRC according to claim 4, characterized in that, The second LADRC controller includes a second expanded state observer and a second linear state error feedback controller. The second expanded state observer monitors in real time the magnitude, dynamic changes, and system disturbances of the average inlet pressure of all units participating in grid connection during the throttling-to-grid connection process, effectively extracting dynamic information and transmitting it to the second linear state error feedback controller. The second linear state error feedback controller generates control quantities based on the dynamic changes of the average inlet pressure of all units and system disturbance information to adjust the opening of the main pipe regulating valve for rapid compensation and suppression of disturbances, achieving high-precision control of the average inlet pressure of all units, ensuring stable pressure ratios and safe operation of each unit. The linear state error feedback control law of the second linear state error feedback controller satisfies: Where e3 is the average compressor inlet pressure of all grid-connected extraction units obtained using the second extended state observer. The deviation between the estimated value and the set value of the second LADRC controller, where u2 is the control output of the second LADRC controller. The average compressor inlet pressure of each extraction unit obtained using the second expansion state observer. The estimated value, express The estimated value of the differential. b1 is the disturbance estimate, and b2 is the gain of the second LADRC controller. This is the control bandwidth of the second LADRC controller; The method for operating the second extended state observer satisfies: Where e4 represents the average compressor inlet pressure of all pumping units participating in grid connection. The deviation between the measured value and the estimated value, This represents the observation bandwidth of the second extended state observer.
Citation Information
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